Question

find the area of each.
29)
1.9 cm
6 cm

30)
1.9 m
3 m
3.9 m

31)
7.8 cm
8.6 cm

translation: 8 units right and 6 units up
d) reflection across the y - axis

Explanation:

Problem 29: Area of Triangle

Step1: Identify Triangle Type

The triangle is a right triangle (marked with right angle) with legs \( b = 1.9 \, \text{cm} \) and \( h = 6 \, \text{cm} \).

Step2: Apply Triangle Area Formula

The formula for the area of a triangle is \( A = \frac{1}{2} \times \text{base} \times \text{height} \).
Substitute \( b = 1.9 \) and \( h = 6 \):
\( A = \frac{1}{2} \times 1.9 \times 6 \)
\( A = 0.5 \times 11.4 \)
\( A = 5.7 \, \text{cm}^2 \)

Problem 30: Area of Trapezoid

Step1: Identify Trapezoid Dimensions

The trapezoid has bases \( a = 1.9 \, \text{m} \), \( b = 3.9 \, \text{m} \), and height \( h = 3 \, \text{m} \).

Step2: Apply Trapezoid Area Formula

The formula for the area of a trapezoid is \( A = \frac{1}{2} \times (a + b) \times h \).
Substitute \( a = 1.9 \), \( b = 3.9 \), \( h = 3 \):
\( A = \frac{1}{2} \times (1.9 + 3.9) \times 3 \)
\( A = 0.5 \times 5.8 \times 3 \)
\( A = 2.9 \times 3 \)
\( A = 8.7 \, \text{m}^2 \)

Problem 31: Area of Parallelogram

Step1: Identify Parallelogram Dimensions

The parallelogram has base \( b = 8.6 \, \text{cm} \) and height \( h = 7.8 \, \text{cm} \).

Step2: Apply Parallelogram Area Formula

The formula for the area of a parallelogram is \( A = \text{base} \times \text{height} \).
Substitute \( b = 8.6 \) and \( h = 7.8 \):
\( A = 8.6 \times 7.8 \)
\( A = 67.08 \, \text{cm}^2 \)

Answer:

s:

1. \( \boldsymbol{5.7 \, \text{cm}^2} \)
2. \( \boldsymbol{8.7 \, \text{m}^2} \)
3. \( \boldsymbol{67.08 \, \text{cm}^2} \)